CHAPTER 6:

Hydrographs

Engineering Hydrology (ECIV 4323)

-1

Instructor:

Prof. Dr. Yunes Mogheir

2020

Introduction

Previous Chapter estimation of long-term runoff was examined

the present chapter examines in detail the short-term runoff phenomenon by the storm hydrograph or flood hydrograph or simply Hydrograph

The runoff measured at the stream-gauging station will give a typical hydrograph as shown in Fig. 6.1

- The flood hydrograph is formed as a result of uniform rainfall of duration, D,. over a catchment.

- The Hydrograph (Figure 6.1) has three characteristic regions:

(i) the rising limb AB, joining point A, the starting point of the rising curve and point B, the point of inflection,

(ii) the crest segment BC between the two points of inflection with a peak P in between,

(iii) the falling limb or depletion curve CD starting from the second point of inflection C.

Factor Influencing the Hydrograph:

- Generally, the climatic factors control the rising limb

- Catchment characteristics determine the recession limb

The shape of the basin: influences the time taken for water from the remote parts

of the catchment to arrive at the outlet. Thus the occurrence of the peak and hence

the shape of the hydrograph are affected by the basin shape. Fan-shaped, i.e.

nearly semi-circular shaped catchments give high peak and narrow hydrographs

while elongated catchments give broad and low-peaked hydrographs.

SIZE:

•The peak discharge is less in small catchment.

•The time base of the hydrographs from larger basins will be larger than

those of corresponding hydrographs from smaller basins.

•The duration of the surface runoff from the time of occurrence of the peak

will be higher in large catchments.

SLOPE:

• Large stream slopes give rise to quicker depletion of storage and hence result in

steeper recession limbs of hydrographs. This would obviously result in a smaller

time base.

• The basin slope is important in small catchments where the overland flow is

relatively more important. In such cases the steeper slope of the catchment results

in larger peak discharges.

DRAINAGE DENSITY

•A large drainage density creates situation conducive

for quick disposal of runoff down the channels. This

fast response is reflected in a pronounced peaked

discharge.

•In basins with smaller drainage densities, the

overland flow is predominant and the resulting

hydrograph is squat with a slowly rising limb (Fig.

6.3).

the essential components of a hydrograph are:

(i) the rising limb,

(ii) the crest segment, and

(iii) the recession limb.

D.R.

baseflow

Falling limb

crest

Rising

limb

Q (m3/s)

Time

Concentration

curve

Recession

curve

6.3 COMPONENTS OF A HYDROGRAPH

Inflection Point

Rising Limb

The rising limb of a hydrograph (concentration curve) represents the increase in discharge due to the gradual building up of storage in channels and over the catchment surface.

As the storm continues more and more flow from distant parts reach the basin outlet. At the same time the infiltration losses also decrease with time.

Crest

The peak flow occurs when the runoff from various parts of the catchment at the same time contribute the maximum amount of flow at the basin outlet.

Generally for large catchments, the peak flow occurs after the end of rainfall,

the time interval from the centre of mass of rainfall to the peak being essentially controlled by basin and storm characteristics.

Recession Limb

It extends from the point of inflection at the end of the crest segment to the start of the natural groundwater flow

It represents the withdrawal of water from the storage built up in the basin during the earlier phases of the hydrograph.

The starting point of the recession limb (the point of inflection) represents the condition of maximum storage.

Since the depletion of storage takes place after the end of rainfall, the shape of this part of the hydrograph is independent of storm characteristics and depends entirely on the basin characteristics.

The storage of water in the basin exists as

- surface storage, which includes both surface detention and channel storage,

-interflow storage, and

-groundwater storage, i.e. base-flow storage.

Barnes (1940) showed that the recession of a storage can be expressed as

which Q0: the initial discharge and

Qt :are discharges at a time interval of t days;

K: is a recession constant of value less than unity.

Previous Equation can also be expressed in an alternative form of the exponential decay as

where a =-In K,

The recession constant K; can be considered to be made up of three components to take care of the three types of storages as:

K= Krs . Kri . Krb

where Krs = recession constant for surface storage (0.05 to 0.20),

Kri= recession constant for interflow (0.50 to 0.85) and

Krb = recession constant for base flow (0.85 to 0.99)

Example

6.1

6.4 Base Flow Separation

• In many hydrograph analyses a

relationship between the surface flow

hydrograph and the effective rainfall

(i.e. rainfall minus losses) is sought to

be established.

• The surface flow hydrograph is

obtained from the total storm

hydrograph by separating the quick-

response flow from the slow response

runoff. It is usual to consider the

interflow.

• The base flow is to be deducted from the total storm hydrograph to obtain the surface flow hydrograph in three methods

- Draw a horizontal line from start of runoff to intersection with recession limb (Point A).

- Extend from time of peak to intersect with recession limb using a lag time, N.

N =0.83 A0.2

Where: A = the drainage area

in Km2 and N = days where

Point B can be located and

determine the end of

the direct runoff .

Method I: Straight line method

METHODS OF BASE-FLOW SEPARATION

Method II:

- In this method the base flow curve existing prior to the beginning of the surface runoff is extended till it intersects the ordinate drawn at the peak (point C in Fig, 6.5). This point is joined to point B by a straight line.

- Segment AC and CB separate the base flow and surface runoff.

- This is probably the most widely used base-flow separation procedure.

time

Q N

A B

C

- In this method the base flow recession curve after the depletion of the flood water is extended backwards till it intersects the ordinate at the point of inflection (line EF in Fig. 6.5), Points A and F are joined by an arbitrary smooth curve.

- This method of base-flow separation is realistic in situations where the groundwater contributions are significant and reach the stream quickly.

- The selection of anyone of the three methods depends upon the local practice and successful predictions achieved in the past.

- The surface runoff hydrograph obtained after the base-flow separation is also known as direct runoff hydrograph (DRH).

Method III

- Figure 6.6. show, the hyetograph of a storm. The initial loss and infiltration losses are subtracted from it. The resulting hyetograph is known' as effective rainfall hyetograph (ERH). It is also known as hyetograph of rainfall excess or supra rainfall.

- Both DRH and ERH represent the same Total quantity but in different units

- ERH is usually in cm/h against time

- The area multiplied by the catchment

Area gives the total volume of

the direct runoff ( total area of DRH)

6.5 EFFECTIVE RAINFALL

6.6 UNIT HYDROGRAPH • The problem of predicting the flood hydrograph resulting from a

known storm in a catchment has received considerable

attention. A large number of methods are pro- posed to solve

this problem and of them probably the most popular and widely

used method is the unit-hydrograph method.

• A unit hydrograph is defined as the hydrograph of direct

runoff resulting from one unit depth (1 cm) of rainfall excess

occurring uniformly over the basin and at a uniform rate for a

specified duration (D hours).

• The term unit here refers to a unit depth of rainfall excess

which is usually taken as 1 cm.

• The duration, being a very important characteristic, is used as

indication to a specific unit hydrograph. Thus one has a 6-h

unit hydrograph, 12-h unit hydrograph, etc. and in general

a D-h unit hydrograph applicable to a given catchment.

The definition of a unit hydrograph implies the following:

- It relates only the direct runoff to the rainfall excess. Hence the volume of water contained in the unit hydrograph must be equal to the rainfall excess.

As 1 cm depth of rainfall excess is considered the area of the unit hydrograph is equal to a volume given by 1cm over the catchment.

- The rainfall is considered to have an average intensity of excess rainfall (ER) of l/D cm/h for the duration D-h of the storm.

- The distribution of the storm is considered to be uniform all over the catchment.

- Fig 6.9 shows a typical 6-h unit hydrograph. Here the duration of the rainfall excess is 6 h

Area under the unit hydrograph = 12.92 X 106 m3

Two basic assumptions constitute the foundations for the unit-hydrograph theory:

(i) the time invariance and

(ii) the linear response.

Time Invariance

This first basic assumption is that the direct-runoff response to a given effective rainfall in a catchment is time-invariant. This implies that the DRH for a given ER in a catchment is always the same irrespective of when it occurs.

Linear Response

- The direct-runoff response to the rainfall excess is assumed to be linear. This is the most important assumption of the unit-hydrograph theory.

- Linear response means that if an input xI (t) causes an output yI (t) and an input .x2 (t) causes an output y2 (t), then an input xl (t) +x2 (t) gives an output y1 (t) +y2(t).

- Consequently, if x2 (t) = r XI (t), then y2 (t) = r yI (t).

- Thus if the rainfall excess in a duration D is r times the unit depth, the resulting DRH will have ordinates bearing ratio r to those of the corresponding D-h unit hydrograph.

- Since the area of the resulting DRH should increase by the ratio r, the base of the DRH will be the same as that of the unit hydrograph.

- If two rainfall excess of D-h duration each occur consecutively, their combined effect is obtained by superposing the respective DRHs with due care being taken to account for the proper sequence of events. (The method of superposition )

- The desired ordinates of the DRH are obtained by multiplying the ordinates of the unit hydrograph by a factor of 3.5 as in Table 6.3.

- Note that the time base of DRH is not changed and remains the same as that of the unit hydrograph.

Application of U-Hydrograph

- D-h U-hydrograph and storm hyetograph are available

- ERH is obtained by deducting the losses

- ERH is divided by M blocks of D-h duration

- Rainfall excesses is operated upon

unit hydrograph successively to get different DHR curves

Solution of Ex.6.6

6.7Derivation of Unit Hydrographs

The area under each DRH is evaluated and the volume of the direct runoff obtained is divided by the catchment area to obtain the depth of ER.

The ordinates of the various DHRs are divided by the respective ER values to obtain the ordinates of the unit hydrograph.

Solution of Example 6.7

- However, N =2.91 days is adopted for

convenience.

- A straight line joining A and B is taken as

the divide line for base-flow separation.

- The ordinates of DRH are obtained by

Subtracting the base flow from the ordinates of the storm hydrograph.

6.8 Unit Hydrographs of Different Duration

Unit hydrograph are derived from simple isolated storms

and if the duration of the various storms do not differ two

much (20% D) >>>> make the average duration of D h.

In practice the unit hydrographs of different duration are

needed (nD).

Two methods are available

1. Method of Superposition

2. the S-Curve

6.8 Unit Hydrographs of Different Duration

Unit hydrograph are derived from simple isolated storms

and if the duration of the various storms do not differ two

much (20% D) >>>> make the average duration of D h.

In practice the unit hydrographs of different duration are

needed (nD).

Two methods are available

1. Method of Superposition

2. the S-Curve

1. Method of Superposition

D-H unit duration is

available and it is

needed to make UH

of nDH, where n is

and integer

Superposing n UH

with each graph

separated from the

previous one by

D h.

2- The S-Curve

Solve Example 6.9 by S-curve method

Solution of Example 6.9 by S-curve method